Terwilliger algebras of wreath products of association schemes

Date
2008-01-01
Authors
Bhattacharyya, Gargi
Major Professor
Advisor
Sung Yell Song
Leslie Hogben
Elgin Johnston
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
Authors
Research Projects
Organizational Units
Mathematics
Organizational Unit
Journal Issue
Series
Department
Mathematics
Abstract

In this thesis, we study the T -algebras of symmetric association schemes that are obtained as the wreath product of H(1, m) for m ≥ 2. We find that the D-class association scheme Kn1&m22;Kn2&m22;&cdots; &m22;KnD formed by taking the wreath product of one-class association schemes Kni = H(1, ni) has the triple-regularity property. We determine the dimension of the T -algebra for the association scheme Kn1&m22;Kn2&m22;&cdots; &m22;KnD . We also show that the wreath power Km&m22;D =Km&m22;Km&m22;&cdots;&m22;Km , D copies of Km, is formally self-dual. We give a complete description of the irreducible T -modules and the structure of T -algebra for Km&m22;D for m ≥ 2 by essentially studying the irreducible modules of 2 copies of Km and then extending it to the general case for D copies of Km. Through these calculations we obtain that the T -algebra for Km&m22;D is MD+1C ⊕C⊕12 DD+1 for m ≥ 3, and MD+1C ⊕C⊕12 DD-1 m = 2.

Comments
Description
Keywords
Citation
Source